Date of Defense

19-11-2024 10:00 AM

Location

F1-2119

Document Type

Thesis Defense

Degree Name

Master of Science in Mathematics

College

College of Science

Department

Mathematical Sciences

First Advisor

Prof. Farrukh Mukhamedov

Keywords

Quantum Markov Chain, Ising model; XY-model; tree.

Abstract

A central open problem in quantum field theory is the construction of a general theory of quantum field, this thesis introduces quantum probability and applies it via the construction of quantum Markov chains on different hierarchical lattices (Cayley trees). Furthermore, these trees correspond to the Ising-XY-Model which then the existence of a unique Markov chain can be utilized to detect phase transitions.

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Nov 19th, 10:00 AM

QUANTUM MARKOV CHAINS RELATED TO CERTAIN LATTICE MODELS

F1-2119

A central open problem in quantum field theory is the construction of a general theory of quantum field, this thesis introduces quantum probability and applies it via the construction of quantum Markov chains on different hierarchical lattices (Cayley trees). Furthermore, these trees correspond to the Ising-XY-Model which then the existence of a unique Markov chain can be utilized to detect phase transitions.